algebra 1 unit 1 days 1 and 2.notebook - ms. morgan's...

Algebra 1 Unit 1 Days 1 and 2.notebook

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Algebra 1Unit 1

Day 1

Relationships between Quantities and Expressions


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MGSE9–12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context.

MGSE9–12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients, in context.

MGSE9–12.A.SSE.1b Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.

Perform arithmetic operations on polynomialsMGSE9–12.A.APR.1 Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations. (For the purpose of this course, operations with polynomials will be limited to the second degree. Higher degree polynomials will be addressed in future courses.)

MGSE9–12.N.Q.1 Use units of measure (linear, area, capacity, rates, and time) as a way to understand problems:a. Identify, use, and record appropriate units of measure within context, within data displays, and on graphs;b. Convert units and rates using dimensional analysis (English–to–English and Metric–to–Metric without conversion factor provided and between English and Metric with conversion factor);c. Use units within multi–step problems and formulas; interpret units of input and resulting units of output.

What Are Our Learning Goals?


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H.O.T.Questions

• How do I interpret parts of an expression in terms of context?

• How are polynomial operations related to operations in the real number system?

• How can polynomials be used to express realistic situations?


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Rationale for the format of this math classStandards‐based classroom

21st Century skillsH.O.T. questions

Standards for Mathematical Practice.

(See Day "0" of School presentation)

Whole Class Discussion


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OpeningStructure of Expressions

2x2 3x 7

2x2, 3x, 7

How many terms? three; trinomial

Factors 2 and x2, 3 and x

Coefficients 2 and 3

Leading Coefficient 2

Constant 7

Degree Second

Terms


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Algebra Tileshttp://mathbits.com/MathBits/AlgebraTiles/AlgebraTiles/AlgebraTiles.html

Opening

Note: “Negative” tiles have the same dimensions, but are red instead.

http://mathbits.com/mathbits/algebratiles/algebratiles/algebratiles.html


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How do we represent algebraic expressions with algebra tiles?

3x2

2x2

2x

4x

56

x2 + 5x + 3

2x2 + 3x 1


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Represent the following expressions using algebra tiles:


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Zero Pairs (Additive Inverses) can be removed from the group without changing the value of a polynomial because zero pairs/additive inverses add up to zero.


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(3x2 + 2x + 2) + (2x2 + x 5)

Represent the following using algebra tiles:

Adding Polynomials


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(3x2 + 2x + 2) + (2x2 + x 5)


The simplified polynomials is: x2 + 3x 4

3x2 + 2x + 22x2 + x 5x2 + 3x 3


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Represent the following with algebra tiles:

(5x2 + 6x 1) + (x2 3x)


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Represent the following with algebra tiles:

(5x2 + 6x 1) + (x2 3x)


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Subtracting Polynomials

(x2 2x + 1) (3x2 4x 1)

Represent the following using algebra tiles


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Subtracting Polynomials

(x2 2x + 1) (3x2 4x 1)Represent the following using algebra tiles

Notice that for the second expression (the minued), we flipped each tile upside down because subtracting means "adding the opposite", which is the same as distributing the negative. 3x2 became 3x2, 4x became 4x, and 1 became 1.

In other words, we first represented the inverse of the second expression and then combined the two expressions.


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Subtracting PolynomialsRepresent the following using algebra tiles

(3x2 + 4x 3) (2x 3)


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Subtracting PolynomialsRepresent the following using algebra tiles

(3x2 + 4x 3) (2x 3)

3x2 + 2xAnswer:


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Multipying Polynomials(x + 1) (2x + 3)

• Use the "L" bracket template to represent the multiplication problem. • Lay out the tiles on the outside the bracket to represent the factors we are multiplying. • x + 1 could be length, and 2x + 3 could be width (or the other way around). • Now fill in the rectangle space with tiles to represent the area.• Remember when we multiply two factors, we, basically, find the area of a rectangle.

x +1

2x + 3

The answer: 2x2 + 5x + 3


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Multipying Polynomials

(x + 2) (x 5)


Answer: x2 + 7x 10


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(x + 2) (4x 5)



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(x + 2) (4x 5)


Answer: 4x2 + 12x 10


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Work Period

Begin The Modeling Framework Task.


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Extension Problem


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Answer the lesson’s H.O.T. questionShare solutions and strategies.

Closing

H.O.T.Questions





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HomeworkPart 1: Classify each as M (monomial), B (binomial), T (trinomial), P (polynomial), or C (constant).

1).______

2).______

3).______

Part 2: Standard Form of Polynomials4.) Circle the problems that are in standard form. If it is not in standard form, re‐write in standard form.

a. ________________

b. ________________

5. Given: How many terms are there? ____What is the leading coefficient? _____What is the coefficient of the 3rd term? ____What is the constant? _____

Part 3: Add these polynomials. Only combine terms that are alike (have the same exponent).6.) 14x + 5+10x + 5

7.) ( =

Part 4: Subtract these polynomials. 8.) (6x + 14)

‐ (9x + 5)

9.) (17x2 + 7x ‐ 14) ‐ (‐6x2 ‐ 5x ‐ 18) =

10) (‐2x2 ‐ 5x + 12) ‐ (x2 + 3x + 12) =


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Algebra 1Unit 1Day 2


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WarmUp

Same or different?

(x + 1)2, x2 + 1, and 2(x + 1)?

Use Algebra Tiles to justify your point.


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MGSE9–12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context.

MGSE9–12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients, in context.

MGSE9–12.A.SSE.1b Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.

Perform arithmetic operations on polynomialsMGSE9–12.A.APR.1 Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations. (For the purpose of this course, operations with polynomials will be limited to the second degree. Higher degree polynomials will be addressed in future courses.)MGSE9–12.N.Q.1 Use units of measure (linear, area, capacity, rates, and time) as a way to understand problems:a. Identify, use, and record appropriate units of measure within

context, within data displays, and on graphs;b. Convert units and rates using dimensional analysis (English–

to–English and Metric–to–Metric without conversion factor provided and between English and Metric with conversion factor);

c. Use units within multi–step problems and formulas; interpret units of input and resulting units of output.

What Are Our Learning Goals?


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H.O.T.Questions





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OpeningWhole Class Discussion

What have we learned so far?


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Work Period

Continue the Modeling Task.


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Extension Problem


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Answer the lesson’s H.O.T. questionsShare solutions and strategies.

Closing

H.O.T.Questions• How do I interpret parts of an expression in terms of context?




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HomeworkPart 1: Multiplying Monomials

1.)

2.)

3.)

4.)

5.) Part 2: Multiplying Binomials

1.) (x + 2) (‐x + 3)

2.) (2x ‐ 5) (x ‐ 15)

3.) (5x ‐ 11) (5x ‐ 11)

4.) (6x + 22) (‐10x + 5)

(11x ‐ 2) (11x + 2)


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algebra 1 unit 1 days 1 and 2.notebook - ms. morgan's...

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